A few years ago I heard a story about a talk given at Stanford by a famous probabilist, perhaps Kai-Lai Chung. The speaker got into some sort of argument with a mathematician in attendance, and called ...

Kurt Gödel in 1931 used $x\Pi a$ where we in contemporary notation would use $(\forall x) A$ or $(x)A$, and $Ex a$ where we would use $(\exists x) A$. I believe that I remember that $\Sigma xA$ has ...

As far as I know, when Poincare formulated his well known conjecture, the original statement was the follwoing: if a closed manifold has the same homology groups as the sphere it is homoeomorphic to ...

I'm writing a paper for real analysis seminar, a paper about Banach-Zarecki theorem and I need some information about the authors.
Stefan Banach - there is no problem to find information about him.
...

In Grothendieck's Sketch of a Programme he spends a few pages discussing polyhedra over arbitrary rings and concludes with some intriguing remarks on specializing polyhedra over their "most singular ...

(1) The condition that a term $a$ be substitutable for another term in an expression can be given a recursive definition. Who first developed such a definition?
(2) One sometimes see the phrase "$a$ ...

The headline already says it: Is anybody (except me) aware of this formula for higher total covariant derivatives of tensor products?
It is the simplest application of the commutative shuffle product ...

I have the distinct memory of having often heard and read that intuitionism was inter alia geared to avoid Cantor's uncountable sets, and it may be that this was Brouwer's plan. But are there accounts ...

May I ask what is the (historical) reason we adopted the $\sigma$-algebra rhetoric instead of $\sigma$-rings (like used in Halmos)? To my knowledge almost all modern measure theory or real analysis ...

Who first introduced the definition of symmetry using functions explicitly? (That is, for instance, a symmetry of a subset $X$ of the plane is a function $F$ from the plane to the plane that preserves ...

The "random" sample is obviously very, very skewed: If you would be asked to name a random conjecture, it probably will be a "famous" conjecture, and the longer a conjecture stands, the more famous it ...

In the early 20th century there was a lot of fuss over the axiom of choice implying that there are Lebesgue non-measurable sets of reals. In his book about The Axiom of Choice, Gregory Moore points to ...

I was wondering who originated the presentation of Verdier duality as an equivalence between categories of sheaves and cosheaves ?
I learnt it reading Jacob Lurie's Higher Algebra and Justin Curry's ...

Recently, it became apparent to me that I was not the only one who always first thought in terms of cap product before actually computing a cup product. There is no denying this is evil, but I found ...

In the paper Zur Hilbertschen Beweistheorie, John Von Neumann has proposed a consistency proof for
a fragment of first-order arithmetic (the fragment without induction and with
the successor axioms ...

Bounded Zermelo set theory, and many variants named for MacLane in some way, are used in equiconsistency proofs for Simple Theory of Types plus infinity, and for the Elementary Theory of the Category ...

Who is the most ancient mathematician of which we have a photograph?
(or, in the same vein, what is the oldest photograph of a mathematician)
A quick search on MacTutor History of Mathematics gives ...

I would love to understand the famous formula $g_{ij}(x) = \delta_{ij} + \frac{1}{3}R_{kijl}x^kx^l +O(||x||^3)$, which is valid in Riemannian normal coordinates and possibly more general situations.
...

When the Stirling numbers of the second kind were introduced by James Stirling in 1730, it was not combinatorially; rather, the numbers ${n \brace k}$ were defined via the polynomial identity
$$
x^n = ...

So we've been using summations at least since the dawn of calculus. I'm wondering how the process of summing a function came to be known? Are there events that led to the invention of the summation ...

Rolle published what we today call Rolle's theorem about 150 years before the arithmetization of the reals. Unfortunately this proof seems to have been buried in a long book [Rolle 1691] that I can't ...

In his proof of the Shannon capacity of a graph, Lovasz utilizes a coordinate representation of the pentagon (namely an orthonormal representation). Who first utilized a coordinate representation for ...